ISO 15288 covers the System lifecycle, while ISO 12207 covers the Software lifecycle. As of 2008, the two are "harmonized for concurrent use". For instance, 12207 can be used "either alone or in conjunction with ... 15288"
In a bit more detail, what this means is that 15288 covers all aspects of developing a system, where examples of system components are hardware, software, people, or resources. When a system component is software, the processes described in 12207 (should) take over.
So, to answer your question, your 12207 software-specific process documents should only need to change where they cover the interfaces between software and non-software components. This might include such things as:
- documenting software dependencies on hardware
- ensuring that your organization has a way to provide personnel with any training needed to use the software
- describing the impact of provision, transportation, or maintenance of resources controlling, or controlled by, the software
... and so on.